I. Interactions of high-affinity cationic blockers with the translocation pores of B. anthracis, C. botulinum, and C. perfringens binary toxins Recently, we have introduced cationic beta-cyclodextrin derivatives as highly effective and potentially universal blockers of three binary bacterial toxins: anthrax toxin of Bacillus anthracis, C2 toxin of Clostridium botulinum, and iota toxin of Clostridium perfringens. The binary toxins are made of two separate components: the enzymatic A component, which acts on certain intracellular targets, and the binding/translocation B component, which forms oligomeric channels in the target cell membrane. This year we studied the voltage and salt dependence of the rate constants of binding and dissociation reactions of two structurally different beta-cyclodextrins (AmPrbCD and AMBnTbCD) in the PA63, C2IIa, and Ib channels (B components of anthrax, C2, and iota toxins, respectively). With all three channels, the blocker carrying extra hydrophobic aromatic groups on the thio-alkyl linkers of positively charged amino groups, AMBnTbCD, demonstrated significantly stronger binding compared with AmPrbCD. This effect is seen as an increased residence time of the blocker in the channels, whereas the time between blockages characterizing the binding reaction on-rate stays practically unchanged. Surprisingly, the voltage sensitivity, expressed as a slope of the logarithm of the blocker residence time as a function of voltage, turned out to be practically the same for all six cases studied, suggesting structural similarities among the three channels. Also, the more effective AMBnTbCD blocker shows weaker salt dependence of the binding and dissociation rate constants compared with AmPrbCD. By estimating the relative contributions of the applied transmembrane field, long-range Coulomb, and salt-concentration-independent short-range forces, we found that the latter represent the leading interaction, which accounts for the high efficiency of blockage. In a search for the putative groups in the channel lumen that are responsible for the short-range forces, we performed measurements with the F427A mutant of PA63, which lacks the functionally important phenylalanine clamp. We found that the on-rates of the blockage were virtually conserved, but the residence times and, correspondingly, the binding constants dropped by more than an order of magnitude, which also reduced the difference between the efficiencies of the two blockers. Thus our quantitative analysis allowed us to discriminate between the physical forces defining the strength of interactions and, therefore, to help directed search for efficient antidotes. II. VDAC regulation by tubulin: Role of the membrane Elucidating molecular mechanisms by which lipids regulate protein function within biological membranes is critical for understanding many cellular processes. The ability of lipids to regulate proteins arises from both specific chemical features of lipid molecules and mechanical and structural properties of the lipid bilayer. Structural, compositional, and elastic parameters of lipid membranes are known to have a strong influence on the function of membrane proteins, such as ion channels, as well as on the interaction of water-soluble proteins with membranes. Recently, we have found that dimeric tubulin, a subunit of microtubules, regulates mitochondrial respiration by blocking the voltage-dependent anion channel (VDAC) of the mitochondrial outer membrane. During this reporting period, we have shown that the mechanism of VDAC blockage by tubulin involves tubulin interaction with the membrane as a critical step. The on-rate of the blockage varies up to 100-fold depending on the particular lipid composition used for bilayer formation in reconstitution experiments and increases with the increasing content of dioleoylphosphatidylethanolamine (DOPE) in dioleoylphosphatidylcholine (DOPC) bilayers. At physiologically low salt concentrations, the on-rate is decreased by the charged lipid. The off-rate of VDAC blockage by tubulin does not depend on the lipid composition. Using confocal fluorescence microscopy, we compared tubulin binding to the membranes of giant unilamellar vesicles (GUVs) made from DOPC and DOPC/ DOPE mixtures. We found that detectable binding of the fluorescently labeled dimeric tubulin to GUV membranes requires the presence of DOPE. We propose that prior to the characteristic blockage of VDAC, tubulin first binds to the membrane in a lipid-dependent manner. We thus reveal a new potent regulatory role of the mitochondrial lipids in control of the mitochondrial outer membrane permeability and hence mitochondrial respiration through tuning VDAC sensitivity to blockage by tubulin. More generally, our findings give an example of the lipid-controlled protein-protein interaction where the choice of lipid species is able to change the equilibrium binding constant by orders of magnitude. III. Physical theory of facilitated transport This year we have concentrated on two topics: (i) the effects of channel/receptor clustering and (ii) intra-membrane cavitation as a mechanism of membrane permeabilization. Various membrane functional units such as receptors, transporters, and channels, whose action necessarily involves capturing diffusing molecules, are often organized into multimeric complexes forming clusters on the cell and organelle membranes. These functional units themselves are usually oligomers of several integral proteins, which have their own symmetry. Depending on the symmetry, they form clusters on different packing lattices. Moreover, local membrane inhomogeneities, e.g., the so-called membrane domains, rafts, stalks, etc., lead to different patterns even within the structures on the same packing lattice. It is clear that the units located at the cluster periphery partially screen the units in the central part of the cluster from diffusing molecules. We were able to formulate a general approach which allows one to quantitatively describe the screening effects. The approach is used to derive simple expressions giving the trapping rates of diffusing molecules by clusters of absorbers on lattices of different packing symmetries. Our analysis shows how the trapping rate changes from the sum of the rates of individual absorbers forming the cluster to the decreasing effective collective trapping rate as the number of absorbers in the cluster increases and/or the inter-absorber distance decreases. Numerical tests demonstrate good agreement between the rates predicted by the theory and obtained from Brownian dynamics simulations for clusters of different shapes, lattice symmetries, and sizes. The study of intra-membrane cavitation (IMC) was motivated by recent publications in which it was suggested that this type of cavitation, rather than homogeneous cavitation, is crucial in ultrasound-induced membrane permeabilization and traumatic brain injury. We have focused on the thermodynamics of IMC, namely, on the minimum work required to form an intra-membrane cavity. The minimum work can be separated into two parts, one that depends on the volume and number of gas molecules in the bubble and another that depends on the bubble geometry. Using a simplified assumption about the cavity shape, the geometry-dependent term is derived and minimized at a fixed cavity volume. It was found that the optimized cavity is almost spherical at large bubble volumes, while at small volumes the cavity has a lens-like shape. The optimized shape was used to analyze the minimum work of IMC, which turned out to be significantly smaller than that of the homogeneous cavitation, thus suggesting IMC leading role in formation of membrane defects during ultrasound-induced membrane permeabilization and in traumatic brain injury.